Efficient Consideration of Soft Time Windows in a Large Neighborhood Search for the Districting and Routing Problem for Security Control

  • Bong-Min Kim
  • Christian Kloimüllner
  • Günther R. Raidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10197)


For many companies it is important to protect their physical and intellectual property in an efficient and economically viable manner. Thus, specialized security companies are delegated to guard private and public property. These companies have to control a typically large number of buildings, which is usually done by teams of security guards patrolling different sets of buildings. Each building has to be visited several times within given time windows and tours to patrol these buildings are planned over a certain number of periods (days). This problem is regarded as the Districting and Routing Problem for Security Control. Investigations have shown that small time window violations do not really matter much in practice but can drastically improve solution quality. When softening time windows of the original problem, a new subproblem arises where the minimum time window penalty for a given set of districts has to be found for each considered candidate route: What are optimal times for the individual visits of objects that minimize the overall penalty for time window violations? We call this Optimal Arrival Time Problem. In this paper, we investigate this subproblem in particular and first give an exact solution approach based on linear programming. As this method is quite time-consuming we further propose a heuristic approach based on greedy methods in combination with dynamic programming. The whole mechanism is embedded in a large neighborhood search (LNS) to seek for solutions having minimum time window violations. Results show that using the proposed heuristic method for determining almost optimal starting times is much faster, allowing substantially more LNS iterations yielding in the end better overall solutions.


Districting and routing problem for security control Vehicle routing problem Soft time windows Dynamic programming Linear programming 


  1. 1.
    Davidovic, T., Hansen, P., Mladenovic, N.: Variable neighborhood search for multiprocessor scheduling problem with communication delays. In: Proceedings of MIC, vol. 4, pp. 737–741 (2001)Google Scholar
  2. 2.
    Fagerholt, K.: Ship scheduling with soft time windows: an optimisation based approach. Eur. J. Oper. Res. 131(3), 559–571 (2001)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Hashimoto, H., Ibaraki, T., Imahori, S., Yagiura, M.: The vehicle routing problem with flexible time windows and traveling times. Discrete Appl. Math. 154(16), 2271–2290 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ibaraki, T., Imahori, S., Kubo, M., Masuda, T., Uno, T., Yagiura, M.: Effective local search algorithms for routing and scheduling problems with general time-window constraints. Transp. Sci. 39(2), 206–232 (2005)CrossRefGoogle Scholar
  5. 5.
    Ioachim, I., Gelinas, S., Soumis, F., Desrosiers, J.: A dynamic programming algorithm for the shortest path problem with time windows and linear node costs. Networks 31(3), 193–204 (1998)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Pisinger, D., Ropke, S.: Large neighborhood search. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, chap. 13, pp. 399–419. Springer, Heidelberg (2010)Google Scholar
  7. 7.
    Prischink, M.: Metaheuristics for the districting and routing problem for security control. Master’s thesis, TU Wien, Institute of Computer Graphics and Algorithms, May 2016. https://www.ac.tuwien.ac.at/files/pub/prischinkd_16.pdf, supervised by G. Raidl, B. Biesinger, and C. Kloimdllner
  8. 8.
    Prischink, M., Kloimüllner, C., Biesinger, B., Raidl, G.R.: Districting and routing for security control. In: Blesa, M.J., Blum, C., Cangelosi, A., Cutello, V., Nuovo, A.D., Pavone, M., Talbi, E.G. (eds.) HM 2016. LNCS, vol. 9668, pp. 87–103. Springer, Heidleberg (2016). doi:10.1007/978-3-319-39636-1_7 Google Scholar
  9. 9.
    Taillard, É., Badeau, P., Gendreau, M., Guertin, F., Potvin, J.Y.: A tabu search heuristic for the vehicle routing problem with soft time windows. Transp. Sci. 31(2), 170–186 (1997)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Bong-Min Kim
    • 1
    • 2
  • Christian Kloimüllner
    • 1
  • Günther R. Raidl
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsTU WienViennaAustria
  2. 2.Research Industrial Systems EngineeringConcorde Business Park FSchwechatAustria

Personalised recommendations